Group #16786621 — subgroups

Subgroups — #16786621

Order 3328.

282 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131043	C₂	1	1	yes	maximal, characteristic
2	#13131037	C₂	1	1	yes	maximal, characteristic
3	#13129754	C₂	1	4	yes	maximal, complemented
4	#13113118	C₂	1	1	yes	maximal, characteristic
5	C₂×#88098	C₄	1	2	yes	—
6	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	—
7	#11718346	C₄	1	2	yes	—
8	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	#11718258	C₄	1	2	yes	—
10	#11718257	C₄	1	2	yes	—
11	#11718231	C₂²	1	2	yes	—
12	#11718231	C₂²	1	2	yes	—
13	C₈²×C₁₃	C₄	1	1	yes	characteristic
14	#11718046	C₂²	1	2	yes	—
15	C₈×#1055	C₄	1	1	yes	characteristic
16	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#6092	C₂×C₄	1	4	yes	—
20	C₂×#6092	C₂×C₄	1	4	yes	—
21	#88098	—	2	4	no	—
22	D₁₃⋊C₁₆	C₈	1	8	yes	complemented
23	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	#88060	—	2	2	no	—
26	#88054	—	2	2	no	—
27	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄×#1055	C₂×C₄	1	2	yes	—
30	C₄×#1055	C₂³	1	1	yes	characteristic
31	#11405	—	13	1	no	maximal, Sylow
32	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
33	C₂×C₄×D₁₃	M₁₆	1	2	yes	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
37	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
39	C₄×Dic₁₃	M₁₆	1	2	yes	—
40	C₂×#1055	—	2	2	no	—
41	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
42	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
43	C₈×D₁₃	C₂×C₈	1	4	yes	—
44	C₈×D₁₃	M₁₆	1	4	yes	—
45	#6092	—	2	4	no	—
46	#6092	C₂×C₈	1	8	yes	—
47	C₄×M₃₂	—	13	1	no	—
48	C₂×#346	—	13	1	no	—
49	#1450	—	13	1	no	—
50	#1313	—	13	4	no	—
51	C₂²×D₁₃	#97	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
54	C₂×Dic₁₃	#97	1	2	yes	—
55	C₂×Dic₁₃	#97	1	1	yes	characteristic
56	C₄×D₁₃	—	4	2	no	—
57	C₄×D₁₃	C₄×C₈	1	2	yes	—
58	C₄×D₁₃	#97	1	2	yes	—
59	C₈×C₁₃	—	4	2	no	—
60	C₈×C₁₃	C₄×C₈	1	2	yes	—
61	C₈×C₁₃	#97	1	2	yes	—
62	#1055	—	4	2	no	—
63	#1055	C₂²×C₈	1	2	yes	—
64	#1055	C₂×M₁₆	1	2	yes	—
65	C₂×M₃₂	—	13	2	no	—
66	C₂²×C₁₆	—	13	2	no	—
67	#431	—	13	2	no	—
68	C₂×C₄×C₈	—	13	1	no	—
69	#346	—	13	2	no	—
70	#346	—	13	2	no	—
71	#346	—	13	2	no	—
72	C₄×C₁₆	—	13	2	no	—
73	#322	—	13	2	no	—
74	C₈²	—	13	1	no	—
75	C₈²	#261	1	1	yes	characteristic
76	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
77	C₂×D₁₃	—	2	2	no	—
78	C₂×D₁₃	#322	1	2	yes	—
79	C₄×C₁₃	—	2	2	no	—
80	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
81	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
82	Dic₁₃	—	2	2	no	—
83	Dic₁₃	#322	1	2	yes	—
84	C₂²×C₈	—	13	1	no	—
85	C₂²×C₈	—	13	1	no	—
86	C₂×C₄²	—	13	1	no	—
87	M₃₂	—	26	4	no	—
88	C₂×C₁₆	—	13	8	no	—
89	C₂×C₁₆	—	13	4	no	—
90	C₂×C₁₆	—	13	4	no	—
91	C₄⋊C₈	—	26	2	no	—
92	C₂²⋊C₈	—	26	2	no	—
93	C₄×C₈	—	13	1	no	—
94	C₄×C₈	—	13	1	no	—
95	C₄×C₈	—	13	1	no	—
96	C₄×C₈	—	13	2	no	—
97	C₄×C₈	C₂×#261	1	2	yes	—
98	C₄×C₈	C₂×#261	1	1	yes	characteristic
99	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
100	C₂×C₁₃	#2110	1	2	yes	—
101	D₁₃	—	2	2	no	—
102	C₂²×C₄	—	13	1	no	—
103	C₂²×C₄	—	13	2	no	—
104	C₂×C₈	—	2	2	no	—
105	C₂×C₈	—	13	1	no	—
106	C₂×C₈	—	13	1	no	—
107	C₂×C₈	—	13	4	no	—
108	C₂×C₈	—	13	4	no	—
109	C₂×C₈	—	26	2	no	—
110	C₂×C₈	C₄×#261	1	1	yes	characteristic
111	C₂×C₈	C₄×#261	1	1	yes	characteristic
112	C₄²	—	13	2	no	—
113	C₄²	—	13	1	no	—
114	C₄²	C₂²×#261	1	1	yes	characteristic
115	C₁₆	—	13	8	no	—
116	C₁₆	—	26	4	no	—
117	C₁₃	#11405	1	1	yes	characteristic, complemented, Sylow
118	C₂³	—	13	1	no	—
119	C₂×C₄	—	13	1	no	—
120	C₂×C₄	—	13	2	no	—
121	C₂×C₄	—	13	2	no	—
122	C₂×C₄	—	13	2	no	—
123	C₂×C₄	—	52	2	no	—
124	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
125	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
126	C₈	—	4	2	no	—
127	C₈	—	13	2	no	—
128	C₈	—	13	2	no	—
129	C₈	—	52	2	no	—
130	C₈	C₈×#261	1	2	yes	—
131	C₈	#88100	1	2	yes	—
132	C₂²	—	13	2	no	—
133	C₂²	—	26	2	no	—
134	C₂²	#11719047	1	1	yes	characteristic
135	C₄	—	2	2	no	—
136	C₄	—	13	2	no	—
137	C₄	—	26	2	no	—
138	C₄	C₂×C₈×#261	1	1	yes	characteristic
139	C₄	C₂×#88100	1	1	yes	characteristic
140	C₂	—	26	2	no	—
141	C₂	#13130032	1	1	yes	characteristic
142	C₂	#13131058	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13131043

C₂

yes

maximal, characteristic

#13131037

C₂

yes

maximal, characteristic

#13129754

C₂

yes

maximal, complemented

#13113118

C₂

yes

maximal, characteristic

C₂×#88098

C₄

yes

—

C₂×D₁₃⋊C₁₆

C₄

yes

—

#11718346

C₄

yes

—

C₄×C₈×D₁₃

C₂²

yes

characteristic

#11718258

C₄

yes

—

#11718257

C₄

yes

—

#11718231

C₂²

yes

—

#11718231

C₂²

yes

—

C₈²×C₁₃

C₄

yes

characteristic

#11718046

C₂²

yes

—

C₈×#1055

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×D₁₃

C₂×C₄

yes

characteristic

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×#6092

C₂×C₄

yes

—

C₂×#6092

C₂×C₄

yes

—

#88098

—

D₁₃⋊C₁₆

C₈

yes

complemented

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

#88060

—

#88054

—

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₈×Dic₁₃

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

characteristic

#11405

—

maximal, Sylow

C₂×C₄×D₁₃

C₄²

yes

characteristic

C₂×C₄×D₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₂×C₈×C₁₃

C₄²

yes

characteristic

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄²

yes

characteristic

C₄×Dic₁₃

M₁₆

yes

—

C₂×#1055

—

C₂×#1055

C₂²×C₄

yes

characteristic

C₂×#1055

C₂²×C₄

yes

characteristic

C₈×D₁₃

C₂×C₈

yes

—

C₈×D₁₃

M₁₆

yes

—

#6092

—

#6092

C₂×C₈

yes

—

C₄×M₃₂

—

C₂×#346

—

#1450

—

#1313

—

C₂²×D₁₃

#97

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×Dic₁₃

#97

yes

—

C₂×Dic₁₃

#97

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

C₄×C₈

yes

—

C₄×D₁₃

#97

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄×C₈

yes

—

C₈×C₁₃

#97

yes

—

#1055

—

#1055

C₂²×C₈

yes

—

#1055

C₂×M₁₆

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#431

—

C₂×C₄×C₈

—

#346

—

#346

—

#346

—

C₄×C₁₆

—

#322

—

C₈²

—

C₈²

#261

yes

characteristic

C₂²×C₁₃

C₂×#97

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

#322

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄×C₈

yes

characteristic

C₄×C₁₃

C₂×#97

yes

characteristic

Dic₁₃

—

Dic₁₃

#322

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×#261

yes

—

C₄×C₈

yes

C₂×C₁₃

yes

100

C₂×C₁₃

#2110

yes

—

101

D₁₃

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

C₄×#261

yes

characteristic

111

C₂×C₈

C₄×#261

yes

characteristic

112

C₄²

—

113

C₄²

—

114

C₄²

C₂²×#261

yes

characteristic

115

C₁₆

—

116

C₁₆

—

117

C₁₃

#11405

yes

characteristic, complemented, Sylow

118

C₂³

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

D₁₃⋊M₁₆

yes

—

125

C₂×C₄

C₂×C₄×#261

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

C₈×#261

yes

—

131

C₈

#88100

yes

—

132

C₂²

—

133

C₂²

—

134

C₂²

#11719047

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

C₂×C₈×#261

yes

characteristic

139

C₄

C₂×#88100

yes

characteristic

140

C₂

—

141

C₂

#13130032

yes

characteristic

142

C₂

#13131058

yes

—

	subgroup	G/H
center	C₂×C₈	C₄×#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂²×D₁₃	#97
cosocle	C₄×#1055	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	#11405
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₈

C₄×#261

commutator

C₄×C₁₃

C₂×C₄×C₈

Frattini

C₄²

C₂²×#261

Fitting

C₈²×C₁₃

C₄

socle

C₂²×C₁₃

C₂×#97

C₂²×D₁₃

C₂³

C₈²

C₁₃

G ▷ C₄×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₈ ◁ C₈²

N	H ≅ G/N	type
3. #13129754	C₂	semidirect
22. D₁₃⋊C₁₆	C₈	semidirect
117. C₁₃	#11405	semidirect

H ≅ G/N

type

3. #13129754

C₂

semidirect

22. D₁₃⋊C₁₆

C₈

semidirect

117. C₁₃

#11405

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13131043	2
#13131037	2
#13129754	2
#13113118	2
#11405	13

subgroup

index

Subgroups — #16786621

Conjugacy classes of subgroups

Complements

Maximal subgroups